An Immerman-Szelepcsényi Story

As a grad student in the late 80's I had the opportunity to witness many great and often surprising theorems in computational complexity. Let me tell you about one of them, the Immerman-Szelepcsényi result that nondeterministic space is closed under complement. I wish I had the original emails for this story but instead I'm working from memory and apologies if I get some of the details wrong. I'm expanding from a short version from the early days of this blog.

I started my graduate work at UC Berkeley in 1985 and then moved to MIT in the summer of '86, following my advisor Michael Sipser. In the summer of 1987, Neil Immerman, then at Yale, proved his famous result building on his work in descriptive complexity In those days you didn't email papers, he made copies and sent them by US postal mail to several major researchers in complexity including Sipser. But Sipser was away for the summer, I believe in Russia, and the paper sat in his office.

Immerman also sent the paper to a Berkeley professor, probably Manuel Blum, who gave it to one of his students who decided to speak about the result in a student-led seminar. I forgot who was the student, maybe Moni Naor. I was still on the Berkeley email list so I got the talk announcement and went into complexity ecstasy over the news. I asked Moni (or whomever was giving the talk) if he could tell me details and he sent me a nice write-up of the proof. Given the importance of the result, I sent the proof write-up out to the MIT theory email list.

Guess who was on the MIT theory list? Neil Immerman. Neil wrote back with his own explanation of the proof. Neil explained how it came out of descriptive complexity but as a pure write-up of a proof of the theorem, Moni did an excellent job.

We found out about Robert Szelepcsényi when his paper showed up a few months later in the Bulletin of the European Association for Theoretical Computer Science. Szelepcsényi came to the problem from formal languages, whether context-sensitive languages (nondeterministic linear space) was closed under complement. Szelepcsényi, an undergrad in Slovakia at the time, heard about the problem in a class he took. Szelepcsényi's proof was very similar to Immerman. Szelepcsényi's paper took longer to get to US researchers but likely was proven and written about the same time as Immerman.

Even though both papers were published separately we refer to the result as Immerman-Szelepcsényi and is now just some old important theorem you see in introductory theory classes.
Computational Complexity published first on Computational Complexity